Question

A right rectangular prism has an area of 20 square units and a height of 3 units. What is the volume?

Answer 1

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Answer 2

The area of a right rectangular prism is given by the formula:

Area = 2lw + 2lh + 2wh

We are given that the area is 20 square units and the height is 3 units. If we substitute these values into the formula, we have:

20 = 2lw + 2l(3) + 2w(3)

Simplifying this equation, we get:

20 = 2lw + 6l + 6w

Next, we can factor out a 2 from the first two terms:

20 = 2(lw + 3l) + 6w

Then, we can subtract 6w from both sides of the equation:

20 - 6w = 2(lw + 3l)

Dividing both sides by 2 gives:

10 - 3w = lw + 3l

Next, we can factor out an l from the terms on the right-hand side:

10 - 3w = l(w + 3)

Since the left-hand side is a constant, the right-hand side must also be a constant. Therefore, we have:

w + 3 = 0

Solving for w gives:

w = -3

Since the width cannot be negative, we can conclude that the width must be 3 units.

Now, we can substitute the values of l = 20 and w = 3 into the formula for volume of a right rectangular prism:

Volume = lwh

Volume = 20(3)(3) = 180 cubic units

Therefore, the volume of the right rectangular prism is 180 cubic units.